Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, interactive explorations.
Used and loved by over 6 million people
Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.
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\[ \large \begin{align} 51 \times 51 &= {\color{blue}26}{\color{red}01} \\ 52 \times 52 &= {\color{blue}27}{\color{red}04} \\ 53 \times 53 &= {\color{blue}28}{\color{red}09} \\ 54 \times 54 &= {\color{blue}29}{\color{red}16} \\ 55 \times 55 &= {\color{blue}30}{\color{red}25} \\ 56 \times 56 &= {\color{blue}31}{\color{red}36} \\ & \vdots \end{align} \]
What is the value of \( 57 \times 57?\)
Bonus: Can you explain why this pattern appears, and when it breaks?
by
Chung Kevin
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In the diagram, the yellow and red circles are identical and are both centered on the larger circle's diameter.
Which has a larger area?
by
Chung Kevin
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In a 90-question, multiple-choice test, a student gets
- \(+4\) for a correct answer
- \(-1\) for an incorrect attempt.
If the student attempted every single question, can he or she get a total score of exactly 300?
For example, if the student only got 60 correct answers (30 incorrect), then the total score would be \(60\times4 - 30\times1= 210. \)
by
Kalpok Guha
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What mass (in kilograms) on the left side would keep the system in balance?
by
Ahmed Almubarak
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We have two copper spheres of the same radius; one is hollow (vacuum inside) and the other is solid. Initially, both spheres are in a vacuum at the same temperature. Then they are heated up to the same temperature which causes them both to expand.
Which sphere has the greater final radius?
by
Pranshu Gaba
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